A Dynamic Model of the Knee and Lower Limb for Simulating Rising Movements

A two-dimensional dynamical model of the human body was developed and used to simulate muscle and knee-ligament loading during a fast rising movement. The hip, ankle, and toes were each modeled as a simple hinge joint. Relative movements of the femur, tibia, and patella in the sagittal plane were described using a more detailed representation of the knee. The geometry of the model bones was adapted from cadaver data. Eleven elastic elements described the geometric and mechanical properties of the knee ligaments and joint capsule. The patella was assumed to be massless. Smooth hypersurfaces were constructed and used to calculate the position and orientation of the patella during a forward integration of the model. Each hypersurface was formed by applying the principle of static equilibrium to approximate patellofemoral mechanics during the simulation. The model was actuated by 22 musculotendinous units, each unit represented as a three-element muscle in series with tendon. A first-order process was assumed to model muscle excitation-contraction dynamics. Dynamic optimization theory was used to calculate the pattern of muscle excitations that produces a coordinated rising movement from an initial squatting position in minimum time. The calculations support the contention that squatting is a relatively safe exercise for rehabilitation following ACL reconstruction. ACL forces remain less than 20 N for the duration of the task.

Keywords:

• Mathematical Model
• Knee Ligaments
• Rehabilitation
• Dynamic Optimization